Strains in an Elastic Plate Containing an Interference Fit Bolt Near a Free Edge

8/7/2019 Strains in an Elastic Plate Containing an Interference Fit Bolt Near a Free Edge

1/31

"r7 ARL-STRUC-REPORT-400 AR-003-012DEPARTMENT OF DEFENCE

DEFENCE SCIENCE AND TECHNOLOGY ORGANISATIONAERONAUTICAL RESEARCH LABORATORIES

.n MELBOURNE. VICTORIA

I STRUCTURES REPORT 400

STRAINS IN AN ELASTIC PLATE CONTAINING ANINTERFERENCE-FIT BOLT NEAR A FREE EDGE

.TH. UNTr 'SAE--TOA00" -IC.AI INiLUPRUIVIATION gfV=L .. IfS AUT W49RIS.OTO

by ,EPROCUCE AND SELL THIS REPORTG. S. JOST and R. P. CAREY-

'DTICAPPROVED FO R PUBLIC RELEASE 2 17384

NooL

,) COMMONWEALTH OF AUSTRALIA 1984 M 1Og O1 No M4ARCH 1984


2/31

AR-003-012DEPARTMENT OF DEFENCEDEFENCE SCIENCE AND TECHNOLOGY ORGANISATIONAERONAUTICAL RESEARCH LABORATORIES

STRUCTURES REPORT 400

STRAINS IN AN ELASTIC PLATE CONTAINING AN"INTERFERENCE-FIT BOLT NEAR A FREE EDGE

0by

i ~ G. S. JOST and R. P. CAREY

.. O nPSUMMAREYS.i~~npproximation ha v been developed to permit the use o~f elastic theory for a

.r. ~pressurizedhole near the edge of a semi-infi'nite plate to predict strains in one containingan interference-fit lIi.stener. A4:,mpari.son oj"measuredplate strains with those predictedsuch a situation show good agreement.

i Commonwe alth of Australia 1984


3/31

CONTENTSPage No .

1. INTRODUCTION I

2. ELASTIC ANALYSIS I2.1 Pressurized Hole in a Semi-Infinite Plate I2.2 Relationship Between Interface Pressure and Interference 22.3 Onset of Yielding 4

3. EXPERIMENTAL PROGRAM 43.1 Test Specimens 43.2 Test Procedure 43.3 Errors in Strain 5

4. COMPARISON OF MEASURED AN D PREDICTED STRAINS 54.1 Estimation of Vield Incipience 54.2 Comparison of Theory W Experiment 6

5. DISCUSSION 66. CONCLUSIONS 6

REFERENCES,-.3TABLES

* FIGURES

DISTRIBUTION

DOCUMENT CONTROL DATAAccession For'ITIS GPA&IDTIC TABJustif;tionBy _Dpis ribution/Availability Codes

Avail and/orDist Special"'.,AV A,


4/31

"1.NTRODUCTION"Various techniques, including the use of interference-fit fasteners, have been developed in"recent years for improving the fatigue performance of bolted joints, Although such fastenersare now used extensively in modern civil and military aircraft, the basis for their adoption rests

almost wholly upon experimentally observed improvements in fatigue behaviour. Theoretical"support or understanding for this demonstrated improvement remains largely qualitative.-) ~Uncertainties in the stress/strain fields around the Taper-Lok interference-fit fasteners ("used in the F-I I IC aircraft led to the experimental work reported here.and elsewherei Vhereassolutions for elastic stress and strain fields around a hole containing an interference fastenerin a large plate are readily available, the presence of nearby boundaries causes considerabletheoretical difficulty.-,-.. For the present case of a hole near the edge of a semi-infinite plate containing an interference-fit fastener, an approximation has been developed from the exact, related elastic theory for apressurized hole in a geometrically similar plate. Strains predicted from this theory have beencompared with measured experimental strains.


5/31

'WIM.-M-777.77T.-. " - V

Stresses in the x, y directions are found from:, p +) + (a0,-c)cos 20 + 7p sin 20 (5)

UY = (aa+o)-(ap-ae)cos20-7.,e sin 20 (6)where

0 sinh m in a os~ a -cosunless

(y2-a 2 -x 2 )/y > 0when

0=NF sinh msin g 7r =7arsmnc---s .cosh x-cosoThe upper signs of these equations apply when x is positive, the lower signs when x is negative.

For predicting strains in the plate, plane stress conditions have been adopted. The strainsare therefore found from:

E. = Ux- -Cry (7)* and

C J=,-Vp x (8) .where vp is Poisson's ratio for the plate material and Ep is Young's modulus.

2.2 Relation Between Interface Pressure and InterferenceInterference-fit bolts give rise to interface pressure between the bolt surface and the holean d hence to stresses and strains in both the plate and bolt. In axisymmetric situations, such asthat of a hole in an infinite plate or a thick-walled cylinder, exact relations between the uniformpressure generated and the interference ma y be readily found. In the present case, however,interference fits do not result in a uniform interface pressure and so theory based upon the appli-cation of a uniform pressure in the hole cannot be directly applicable. The theory can, however,

be used to effect in an approximate way to calculate the average radial expansion of the hole(together with the corresponding radial contraction of the bolt) and so relate interference withverage interface pressure. The latter can then be used as required in the preceding formulae.In deriving the required relationship between interface pressure and interference, plane stressconditions are assumed for the plate, and plane strain for the bolt. Th e average radial expansionof the hole, up, is found by evaluating the total increase in the circumference of the hole underthe action of the pressure p and dividing this by 21T. Thus, Up is found from

i 27r.,Up r2 d# (9)

where d# is an elemental angle from the hole centre.For plane stress conditions in the plate

2


6/31

where subscript p refers to the plate and a. and a# on the bore of the hole are found from (I)and (2) as,.= -p (11)

Sanda#= p[2(cosh 2 c, -cos 2 P)cosech 2 a,--1] (12)

To permit integration of (12), cos 2 P must be expressed in terms of 0. Referring to Fig. 1,application of the sine rule to ABC results in(d/r)-cos "

In addition, in Ref. 2 it is shown thattan q = (r/a)sin P

Equating these expressions and rearranging givesC."2 Ps II-- sin2 }/(--cos #)

Substituting (i1) and (12) into (10) and performing the integration in (9) yields*pr 2(coth al-- 1)up-1+v 1+ 1+ (13)

where the term in square brackets represents the semi-infinite plate correction to the infiniteplate solution.

For the bolt under the same pressure p, the (uniform) change in radius is readily found fromu -r (14)

and the plane strain condition fromEb = (I +Vb)[(I -- 'b)up- bo (15)

On the surface of the bolt"= p = -p (16)

and hence the displacement is given byt

Eb\ X\"Thesum of the moduli of the displacements up and Ub must equal the interference between boltand plate, so that in terms of a dimensionless interference Adefined by

1U"+ UI1

A - coth aci+vp-- + PI +vb I -2yb (18)

* Th e corresponding formulation fo r plane strain conditions in the plate isUp=rlp+ IV ~ )cotha- ,p))

t For a bolt in plane stress, (17) becomes

E"b,. ,.


7/31

7.

Thus, for given A and knowing the elastic parameters of plate and bolt, the average interfacepressure p may be determined from (18) and used as required in eqns (1) to (8).2.3 Onset of YieldingIn the experimental program to be described, the Taper-Lok interference-fit fasteners

eventually caused yielding of the plate material. It is necessary, therefore, in this elastic analysisto ascertain the location of the onset of yielding and the stage at which it occurs, so that post-yieldexperimental data should be excluded from this analysis.With increasing interference yielding will occur at the hole boundary where the elasticprincipal stresses are given by (11) and (12). For plane stress, the von Mises yield criterionbecomes

. 2+ a82 _-oa ay 2 (19)where ay is the uniaxial yield stress of the plate material. Substitution of (!1) into (19) yields

1 1+_+1 = (20)

from which the value of which maximises a, provides the required solution. It is, from (12),2 (21)

when the limiting (elastic) tangential stress becomes, from (12)%a/p 2 coth2 al - 1. (22)

3. EXPERIMENTAL PROGRAM3.1 Test Specimens

Two specimen configurations were used. Specimen C, illustrated in Fig. 2(a), was a simplesquare plate with a single tapered hole approximately 1 5 diameters from an edge. Th e speci-mens identified as 4/5 and 6/7 and shown in Fig. 2(b) were rectangular with thickened lug endsand each contained two tapered holes, similarly approximately I .5 diameters one from each edge.All holes were finished with an 18 flute tungsten carbide reamer.Th e specimen material was D6ac steel heat treated to achieve an ultimate tensile stress inthe range 1510 to 1650 MPa. The stress-strain characteristics of the material of specimen Care shown in Fig. 5.The tapered bolts fitted into the reamed holes were of the Taper-Lok type, Code2TLHC2-6, and of nominal diameter 3/8 inch (9.525 mm). They were manufactured from H I Isteel and had a nickel-cadmium plating with a wax-like coating of cetyl alcohol. Th e taper ofone in 48 allowed accurate increments in interference to be calculated from measured incrementsin insertion distance.Numerous short gauge length electric resistance strain gauges were bonded to the speci-mens near the holes on both the faces and edges of the specimens. Th e gauge types are givenin Table 1. Their locations are shown in Fig. 2(a) (specimen C), Fig. 3 (specimen 4/5) and Fig. 4(specimen 6/7). With the exception of those gauges located on the specimen edges, the gaugeswere bonded on the faces from which the bolts were inserted in the holes.

3.2 Test ProcedureEach tapered bolt was inserted with firm thumb pressure while the specimen was clampedalong one side in a vice. Interference was increased in steps of approximately 0-01 mm ondiameter by tightening the nuts. Strains and insertion distances were measured-the latter by

a depth micrometer from displacements of the bolt head. Tables 2, 3 and 4 give the values re-corded for each specimen.4


8/31

.. ,., , " 'k , -" - b_ . .,.. -.. . . . .. ,, . .J ,, . , ,... - . .- .- . .. . , .,,. . .

Th e process was continued to 0064 mm interference on diameter in the case of specimen 4/5"andconsiderably higher in specimens C and 6/7. Only data collected within the elastic regimeare presented here.

3.3 Errors in StrainSome of the gauges used had a relatively large grid dimension in one direction. Because

of the strain gradients around the holes introduced by the interference-fit fasteners errors instrain arise as follows:(a) For gauges that are long in the radial direction, the average strain over the radial dimen-sion differs from the strain at the centre of the gauge.or gauges long in the circumferential d irection, the grid near the ends is no t truly

aligned in the circumferential direction.For the same type of gauge, edge distance is increasingly in error near the ends.

"For ype (a) errors it can be shown by integration over the gauge length that, for strainsdistributed as I/r2 , the fractional error in strain at the gauge centre is given byg2/(C __g 2 )*L

where g is the half gauge dimension in the radial direction and c is the distance from hole centreto the gauge centre. Th e error for a I 8 mm long gauge, I 21 mm from the hole, was found tobe +2-2%, the maximum for errors of type (a).Misalignment errors (type (b)) were averaged for 5 positions across one side of a gauge,using Mohr's circle to estimate the individual deviations. The largest error from this cause wasI1.9% for the case of a I 8 mm long gauge located 0.51 mm from the hole. Edge distanceerrors (type (c)) were also averaged on a point to point basis along the gauge. For the example"justgiven the error from this cause was found to be -1 .0%.In summary, the total error from the three causes for the I .8 mm gauge length circum-ferentially aligned 0.51 mm from the hole was -2.8%; total error for I-8 mm gauge radiallyaligned was estimated to be +22/',,: and for gauges of dimension 0.38x0.51 mm the errorfrom these causes was less than 1%.

4. COMPARISON OF MEASURED AND PREDICTED STRAINSBecause the experimental strain data covered both the elastic and plastic regimes, it wasnecessary, for the present elastic analysis, to ascertain the interference beyond which plasticflow at the hole begins. Experimental data in the plastic region were then excluded from subse-* ~quent consideration. The upper limit of the elastic regime was established as follows:

the initial stage of pin insertion often induces a non-linear response in the specimen,strain level rather than insertion distance was used to determine yield incipience. For thispurpose the strain gauge nearest to each hole was adopted as control gaugc. The strain corre-sponding to this condition was computed theoretically for the relevant gauges and used to define"theupper limits of insertion for which valid estimates of elastic strains could be derived., ,In more detail, ayp/ at incipience was evaluated using equations (4), (20) and (22). With eyestimated from Fig. 5 as 1150 MPa, the interface pressures p were calculated to be 588 MPa(for specimen C) and 585 MPa (specimens 4/5 and 6/7). (The corresponding limiting values of


9/31

non-dimensional interference were 0.00552 and 0.00551). The critical strain level at the controlgauges was then found from equations (1) to (8) using common values of elastic parameters forboth bolt and plate of E = 207x 103 MPa and v = 0.3.4.2 Comparison of Theory and Experiment

Th e measured (elastic) strains listed in Tables 2, 3 and 4 for the three specimens are shownplotted in Figs 6 to II against bolt insertion distance. Best fit straight lines are also shown.In some cases the lowest strain readings have no t been included in the analysis because of evidentinconsistency with remaining data arising, possibly, from bolt/hole imperfections.Th e slopes of the fitted lines represent strain per unit bolt insertion distance. These are readilyconverted to strain per unit (dimensionless) interference, and in this form are listed in Tabie 5.They have also been plotted against non-dimensional edge distance for two radial traverses-perpendicular to and parallel with the nearest specimen edge-in Figs 12 and 13 for the singlehole specimen and in Figs 14 an d 15 for the double hole specimens.Th e theoretical curves shown in Figs 12 to 15 have been calculated using equations (1) to (8)together with equation (18), selected values being given in Table 6.

5. DISCUSSIONFigures 12 to 15 inclusive show the agreement between predicted and measured strains tobe good. Some differences are apparent for radial strains in the high strain gradient region

close to the hole, but the reasons for this cannot be identified.The overall substantial agreement noted above indicates that the approximation developedto relate average bolt/hole interface pressure to interference for the present non-axisymmetriccase is quite successful*. Th e approximation must improve as the hole becomes more remotefrom the plate edge, but it must also be expected to begin to break down as the hole becomescloser to the edge. The present study provides no indication as to when this might be expectedto occur.

.9.'

CONCLUSIONSAn approximation has been developed to permit the use of elastic theory for a pressurizedhole near the edge of a semi-infinite plate to predict strains in one containing an interference-fit

fastener. A comparison of measured plate strains and those predicted for a Taper-Lok inter-ference-fit installation shows good agreement.00

Another successful application of the approximation to a plane strain situation is reported inAppendix 5 of Ref. 3.

6


10/31

REFERENCE""1.arey, R. P. Experimental determinations of strain fields resulting from inter-Sference-fit tapered pins. Dept. Supply, Aeronautical Res. Labs.

Structures and Materials Note 377, June 1972.2. Jeffery, G. B. Plane stress and plane strain in bipolar coordinates. Phil. Trans. .".' ~~Roy. Soc. Series A, v. 221, 192 1, pp . 265-293.S3. Mann, J. Y., Improving the fatigue performance of thick aluminium alloy boltedRevill, G. W., and joints by hole cold-expansion and the use of interference-fit steel-'.cLupson, W.tF. bushes. Dept. DefeSpe, AeronauticalRes. Labs. Structures Note 486,S pril 1983. Mel o 3.n

-,,.-,

'-.".4.

'.4." .


11/31

TABLE 1Electric Resistance Strain Gauges

% GaugeGauge Type Specimen Orientation PositionRelative to Hole Length Widthmm mm

'Micromeasurements' 6/7 Circumferential Near tapered hole 7 0-38 0-51A-06-015-DJ-120 4/5 Circumferential Near hole 5 on tra-verse perpendicular

to longitudinal axis 0L8 0Wt1'Micromeasurements' 6/7 Longitudinal Specimen edgeWA-06-125-BT-120 and 4/5 i'Kyowav 67 Radial Near holes 6 and 7 0.3 1

KF-0-I-l4/5 Radial Near holes 4 and 5on longitudinal direc-

*tion traverses 0-3 1 .,0Circumferential As above 0-3 1-8'Kyowa' C Longitudinal Specimen edgeKF-03-C1- 1 n /'Shinkoh' 4/5 Radial Near hole 4 on tra- 0FIP 55-30 verse perpendicularto longitudinal axis 0-5 15'Metal film' C Circumferential Near hole 0.38 0-51CK-0x I5E

Bonding used: M Bond 200 with catalyst.

TABLE 2Strains* Resulting from Insertion of Tapered Bolts-Single Hole Specimen C

Gauge Bolt Insertion Distance(mm)

0'90 127 1-70 1-96 2-581 0-506 0'762 0'960 1'162 1-482

2 1-025 1"580 2'019 2-330 3.0433 0'922 1.498 1.829 2-230 2-8014 0-814 1-339 1-546 1999 2-788

* 10-3-.


12/31

TABLE 3Strains* Resulting from Insertion of Tapered Bolts-Specimen 4/5

Gauge Bolt Insertion Distance (mm)

ThumbTight 0.48 0.99 !60 2"03 2.57 3.051 0.022 0.229 0.450 0.765 1.039 1.304 1-5452 0.002 0.122 0.347 0.693 1.009 1.311 1.5783 -0-055 0.226 0.654 1.269 1.839 2.389 2.816"4 --0.006 0.223 -0.444 -1-163 -1719 -2.342 2-9475 -0.016 0.169 0.604 1-072 1.538 1.994 2.4106 - 0-004 0.157 0.617 1-277 1.816 2.359 2.9097 0-004 0.136 0.450 0.851 1.206 1.579 1.9408 0-000 0.094 0.299 0.568 0.808 1i056 1-294

ThumbTight 0.51 1.02 1"47 1.96 2.44

9 -0-002 -0-130 -0'285 -0"454 -0"623 -0"83110 -0"002 -0"182 -0'416 -0-681 -0"959 -1-27511 0.002 -0"314 -0'834 -1-440 -2"083 -2'71412 0.000 -0'076 -0'645 -1-135 -2'004 -- 2"61513 0.008 0'238 0"536 0-964 1.239 1'76114 -0.093 -0.373 -0"951 -1-450 -1"878 -2"32515 0'012 0.209 0"463 0"698 0-947 1-214

* xlO :1

-.

Li'.


13/31

TABLE 4Strains* Resulting from Insertion of Tapered Bolts-Specimen 6/7

Bolt Insertion Distance (mm)Gauge- - - -

ThumbTight 0-66 1.19 1-85 2-24 2-791 0-002 0-281 0-521 0-893 1.125 1-412

2 -0-004 0.190 0-414 0-797 1-022 1-2653 -0-006 0-265 0-590 1.110 1 40 1-7654 0 00 0 2 0 7 1 2:021 2 -45 0-002 0-543 1-066 1-544 2-216 2-8096 0-002 0-304 0-660 0-988 1-400 1-7587 0.000 -0-314 -0-607 -1-674 -2-016 -2-8838 0.000 0.500 08996 1-658 2-099 2-7609 0.000 0-357 0-616 1-088 1-353 1-750

ThumbTight 0-97 1-32 1-83 2-29 2-9210 -0-002 -0-223 -0-381 -0-544 -0-712 -0-85811 -0-002 -0-194 -0-727 -1-207 -1-898 -2-449

'a~~ 10-3.

TAB EThumb

i*.0 .2 10 5 1 .90. 2 -1.. .2 -- .0040. 1 0 0.14 0 797 .0221.26. - .0 .6 .5 0I 1 .4 -6 .. 0 000 -2900.7 1 1.53 2 021 .47.,,r-.'-.0.0 2 0.43 66 1 5 4 2.16 .80


14/31

%'. '

TABLE 5Measured Strain per Unit Interference Ratio

"Specimen Gauge Non-dimensional Strain/"Number position' Unit interferenceratio 2

C I 2"99 0"2692 1.11 0"5493 1"16 0-5124 1"10 0"531

4/5 I 2.93 0.251"2 I.66 0.2833 1.16 0.501"4 1.10 -0"5665 1"29 0"411"6 114 0-520"7 1-42 0"3408 1-72 02289 1.81 -0.17810 1"51 -0"281I1 1"18 -0-61812 1-14 -0-66913 1-25 0"38914 118 -0-44815 2"93 0"247

6/7 I 2.93 0-2622 1-82 0-2513 1-49 0"348"4 1-16 0-5205 1-16 0-5246 1-46 0-330"7 1-13 -0-6518 I-15 0-5439 1-46 0-33110 1-77 -0-152

II 1-14 -0-543Ratio of distance from hole centre/hole radius.

2 Positive readings are from circumferential gauges. Negativereadings are from radial gauges.

I.

*Ia'* J-a..-a..


15/31

"TABLE 6Theoretical Strain per Unit Interference Ratio

Edge Non- Strain/Unit interference ratiodistance dimensionalratio' position2 Circumferential RadialTraverse Perpendicularo PlateEdge (refer Fig. 12 )

2.99 2.99 (Plate edge) 0.2592"5 0"20820 022815 0"340S1.0 (Hole) 0.669-10 (Hole) 0.669

-1-5 0.305T-2.0 0.171TraverseParallel o Plate Edge (refer Fig. 13 )299 I. 0 (Hole) 0"784

I25 0-48315 0"3102-0 0"135

TraversePerpendicular o Plate Edge (refer Fig. 14)"2-93 2.93 (Plate edge) 0.271 -0.0812.5 0.219 -0.0812-0 0.233 -0.138""4382 -0"332~~ ~-1(Hole) 0.667 -0-0667"0 (Hole) 0.667 -0.667-1"5 0-304 -0"292-2"0 0"171 -0"155

,.....Traverse Parallel o Plate Edge (refer Fig. 15)2"93 1 0(Hole) 0.787 -0-703

1.2 0"532 --046114 0"369 -0.3082"0 0"134 -0"0913"0 0"020 -0-005

SRatio of hole centre to edge distance/hole radius (2.99 for specimenC, 2"93 for specimens 4/5 and 6/7).2 Ratio of distance from hole centre/hole radius.


16/31

= constant

~=constant

020

AA

*%

- Plate edge

'

k,-..

Ut

0.-,,,',


17/31

-7614.2

CentrelineDistance from"GaugeNo. hole edge"6 4 21 (mm)

1:; 1 1 0.64I"3 2 0.51I-3 0.79

4 0.48

Hole taper-reamed to suit Plate thickness = 4.72mm9.525mm nominal diametertaper-lok bolt

.o-.

"FIG.2(a) CONFIGURATION AND GAUGE LOCATIONS-SPECIMEN C

%.,

4.7 14.2

Holes taper-reamed to suitS97.8 I-- -- 9.525mm nominal diametertaper-lok bolt

Al dim nson in-P.TE/

"...:,,-

FI.2()CNIUAINO SEIES45AD67"p


18/31

- x- 74Tf _04- b... .... ...7 T* L . "7 -7 :7

4 12

1 9101 14 'i

Centreline distance from hole edge (mm)Gauge No. 1 - 9.40 Gauge No. 9 - 3.942- 3.20 10 - 2.513- 0.79 11 - 0.894 - 0.51 12 - 0.69%

5- 1.42 13 - 1.2066- 0.66 14 - 0.897 - 2.03 15 - 9.408 - 3.53

FIG. 3 GAUGE LOCATIONS ON SPECIMEN 4/5 -REFER FIG. 2 (b)

JI4ON-

P Igor oil'

Hetrlie ditac f rmooeldemm

Ceteiedstnefo ol.de(m

Gauge No. 1 - 9.40 Gauge No. 6 - 2.232 - 4.00 7 - 0.624113 - 2.37, 8 -0.724 - 0.77 9 - 2.250.5 - 0.77 10 - 3.76

t ~FIG. GAUGE LOCATIONS ON SPECIMEN 6/7 -h REFER FIG. 2 (b)


19/31

1400

1200

1000 -

-'0,

600

Ultimate strength 1528 MPa"0.2%Proof stress 1355 MPa00 -0.1% Proof stress 1308 MPaSElongation6.1%(on 18mm gauge length and 23.2mm 2cross section)

0 I I I I.,,t, 2 4 6 8 1 1Strain (x 10"e)

F .*S T E S TR I HA A T R ST C0OM aterial o p c m nCi6 ac MATERIAL

of speimen


20/31

Gauge 13 13 Gauge 20 Gauge 3X Gauge 4""

.-.- t.-

I I-

ii ." 1.0 2.0Bolt insertion distance (mm)

""*FIG.STRAIN VERSUS INSERTION DISTANCE -"'" ~ ~SPECIMEN C

N.N

Gauge 1SGauge 2

4 2-

x 20.5 1.0 1.5 2.0 2.0 3.0'Bolt insertion distance (mm)

FIG. 7 STRAIN VERSUS INSERTION DISTANCE -S

SPECIMEN C/


21/31

G uge 4X Gauge 52 0 Gauge 13 ee Fig. 32 3Gauge 13}ee0 Gauge 14* Gaugel15

-2-

I-3

Bol insetio ditne(m

44-2

-3-FIG. STRAIN VERSUS INSERTION DISTANCE -%SPECIMEN 4/5


22/31

" -" Gauge 102

0

0 0.5 1.0 1.5 2.0 2.5 3.0Bolt insertion distance (mm)

FIG. 10 STRAIN VERSUS INSERTION DISTANCE -SPECIMEN 6/7

Gauge 53 o "6

0 8

._ 0.5 S 2.0 2.5 3.00 ~Bolt insertion distance (mm)0

V -2i o

-3X " 11

FIG. 11 STRAIN VERSUS INSERTION DISTANCE -SPECIMEN 6/7


23/31

S.A 0.7

0.5...G1o

I0.

S0.6CC

-2 -1 0 1 2 3Dimensionless distance from hole centre

- Present theory (Table 6)0 Experiment (Table 5),..

Z1.. a)

FIG. 12 STRAIN TRAVERSE PERPENDICULAR TO SPECIMEN EDGE -CIRCUMFERENTIAL STRAINS INSINGLE-HOLE SPECIMEN C

"i ~ ~Platedge 0.-0.7

-0.6

0.-

0.30r O.~C 2

* 0.1

0.1-2 -1 0 1 2 3

Dimensionless distance from hole centre* Present theory (Table 6)0 Experiment (Table 5)

FIG. 13 STRAIN TRAVERSE PARALLEL TO SPECIMEN EDGE.-CIRCUMFERENTIAL STRAINS IN SINGLE-HOLE SPECIMEN C


24/31

o 0.7 -cc- 0.6 -

UU1UC0.40*5 Circumferential strain"0.24 -

S= 0.3 -""

0.1-2 -11 2 3Dimensionless distance from hole centre

0.1b

''; -0.2-0.3

-04Radial strain%-0.-0.5-0.6-0.7

Present theory (Table 6)Experimental values:X Hole 4 specimen 4/5 (Table 5)X Hole 513 Hole 6 e / eO Hole 6 specimen 6/7 (Table 5)o Hole7

FIG. 14 STRAIN TRAVERSE PERPENDICULAR TO SPECIMEN EDGE -CIRCUMFERENTIAL AND RADIAL STRAINS IN TWO-HOLE SPEL,,.AEN,


25/31

Plate edge 0.82 0.7S0.6

0.5t 0.5 C'C',umferential strain

(n 0.3.2--

"0.1

"Dimensionless distance from hole centre%

0.1

-0.2

":': -0.2.- 0.

-0.33-.,.

-0.3"-0.4ial strainr"-0.5

-0.6-0.7--0.8

Present theory (Table 6)Experimental values :X Hole 4Hoeole 5 specimen 4/5 (Table 5)0 Hole 7 specimen 6/7 (Table 5)

FIG. 15 STRAIN TRAVERSE PARALLEL TO SPECIMEN EDGE - CIRCUMFERENTIALAND RADIAL STRAINS IN TWO-HOLE SPECIMENS


26/31

"DISTRIBUTION

AUSTRALIA

"DEPARTMENT OF DEFENCECentral Office

Chief Defence ScientistDeputy Chief Defence Scientist (I copy)Superintendent, Science and Technology Programmes|( copy)Controller, Projects and Analytical Studies SDefence Science Representative (U.K.) (Doc. Data sheet only)Counwellor, Defence Science (U.S.A.) (Doc. Data sheet only)Defence Central LibraryDocument Exchange Centre, D.I.S.B. (18 copies)Joint Intelligence OrganisationLibrarian H Block, Victoria Barracks, MelbourneDirector General-Army Development (NSO) (4 copies)

Aeronautical Research LaboratoriesDirectorLibrarySuperintendent-StructuresDivisional File-StructuresAuthors: G. S. Jost

R. P. CareyJ. Y. MannR. JonesM. Heller

Materials Research LaboratoriesDirector/Library

Defence Research CentreLibrary

Navy OfficeNavy Scientific Adviser

Army OfficeArmy Scientific AdviserEngineering Development Establishment, LibraryRoyal Military College Library


27/31

.1ll

Air Force OfficeAir Force Scientific AdviserAircraft Research an d Development Unit

Scientific Flight GroupLibraryTechnical Division LibraryRAAF Academy, Point Cook

Central Studies EstablishmentInformation Centre

DEPARTMENT OF DEFENCE SUPPORTGovernment Aircraft Factories

ManagerLibrary

"DEPARTMENT OF AVIATIONLibraryFlying Operations and Airworthiness Division

STATUTORY AND STATE AUTHORITIES AND INDUSTRYCSIROMaterials Science Division, LibraryTrans-Australia Airlines, LibraryQantas Airways LimitedAnsett Airlines of Australia, LibraryCommonwealth Aircraft Corporation, Library-Hawker de Havilland Aust. Pty Ltd, Bankstown, Library

UNIVERSITIES AND COLLEGESAdelaide Barr Smith LibraryFlinders LibraryLatrobe LibraryMelbourne Engineering Library* onash Hargrave LibraryNewcastle LibrarySydney Engineering LibraryN.S.W. Physical Sciences LibraryQueensland LibraryTasmania Engineering LibraryWestern Australia LibraryR.M.I.T. Library


28/31

CANADACAARC Coordinator StructuresInternational Civil Aviation Organization, Library

* . NR CAeronautical & Mechanical Engineering Library

Universities and CollegesToronto Institute for Aerospace Studies

FRANCEONERA, Library

INDIACAARC Coordinator Structures"DefenceMinistry, Aero Development Establishment, LibraryHindustan Aeronautics Ltd, LibraryNational Aeronautical Laboratory, Information Centre

INTERNATIONAL COMMITTEE ON AERONAUTICAL FATIGUEPer Australian ICAF Representative (25 copies)

ISRAELTechnion-Israel Institute of Technology

Professor A. Buch...

JAPANNational Research Institute for Metals, Fatigue Testing Division

NETHERLANDSNational Aerospace Laboratory (NLR), Library

NEW ZEALANDDefence Scientific Establishment, Library

SW EDENA eronautical Research Institute, L ibrary

SWITZERLANDF-i-W (Swiss Federal Aircraft Factory)

V'O


29/31

UNITED KINGDOMMinistry of Defence, Research, Materials and CollaborationCAARC, SecretaryRoyal Aircraft Establishment"Bedford, LibraryNational Physical Laboratory, Library"NationalEngineering Laboratory, Library"British Library, Lending DivisionCAARC Coordinator, StructuresRolls-Royce LtdAero Division Bristol, LibraryBritish Aerospace"Kingston-upon-Thames, LibraryHatfield-Chester Division, Library

Universities and Colleges"Bristol Engineering LibraryCambridge Library, Engineering DepartmentLondon Professor G. J. Hancock, Aero EngineeringManchester Professor N. Johannesen, Fluid MechanicsNottingham Science LibrarySouthampton LibraryStrathclyde LibraryCranfield Inst. ofTechnology LibraryImperial College Aeronautics Library

UNITED STATES OF AMERICANASA Scientific and Technical Information FacilityApplied Mechanics Reviews

"Universitiesand Colleges.John Hopkins Professor S. Corrsin, EngineeringIowa Professor R. I. StephensIllinois Professor D. C. Drucker

Massachusetts Inst.of Technology M.I.T. Libraries

SPARES (10 copies)

TOTAL (143 copies)


30/31

Department of DefenceDOCUMENT CONTROL DATA

I. a. AR No . I. b. Establishment No. 2. Document Date 3. Task No.AR-003-012 ARL-STRUC-R-400 March, 1984 DST 83/0054. Title S. Security 6. No. PagesSTRAINS IN AN ELASTIC PLATE a. document 14CONTAINING AN INTERFERENCE-FIT BOLT Unclassified _ _ _Nb.itle c. abstract 7. No. RefsNEAR A FREE EDGE U. U. 3U. Author(s) 9. Downgrading InstructionsG. S. JostR. P. Carey

10. Corporate Author and Address II. Authority (as appropriate)Aeronautical Research Laboratories, a.Sponsor c. DowngradingP.O. Box 4331, Melbourne, Vic., 3001 b. Security d. Approval

"12. Secondary Distribution (of this documentApproved for public release

Overseas enquirers outside stated limitations should be referred through ASDIS, Defence Information ServicesBranch, Department of Defence. Campbell Park, CANBERRA, ACT, 2601.13. a. This document may be ANNOUNCED in catalogues and awareness services available to ...No limitations13. b. Citation for other purposes (i.e. casualannouncement) ma y be (select) unrestricted (or) as for 13 a.14. Descriptors 15. COSATI GroupBolted joints Holes (openings) 11130Stress analysis 01030Interference fittingElasticity

16. AbstractAn approximation has been developed to permit the use of elastic theoryfor a pressurized holenear the edge of a semi-infiniteplate to predict strains n one containingan interference-fit astener.A comparison of measured plate strains and those predicted or such a situation shows goodagreement.


31/31

which will no t be added to the DISTIS data base unless specifically requested.16. Abstract (Contd)

17. ImprintAeronautical Research Laboratories, Melbourne

18I.Document Series and Number l9 . Cost Code 20. Type of Report and Period CoveredStructures Report 400 277050

21. Computer Programs Used

0 ~22. Establishment File Ref(s)

Documents

Strains in an Elastic Plate Containing an Interference Fit Bolt Near a Free Edge